Trigonometric Functions and Reference Angles

The video tutorial explains how to determine exact trigonometric function values when given an angle in radians, using reference triangles. It begins with sketching the angle -8PI/3 radians in standard position, identifying the reference angle, and constructing the reference triangle. The tutorial then demonstrates how to calculate the cosine, sine, tangent, secant, cosecant, and cotangent values using the reference triangle. The importance of understanding both degrees and radians is emphasized throughout the lesson.

What is the purpose of using reference triangles in trigonometry?

• To measure angles in a triangle

• To simplify complex numbers

• To determine exact trigonometric function values

• To convert angles from radians to degrees

When sketching -8π/3 radians, in which direction do we rotate?

• Downwards

• Upwards

• Clockwise

• Counterclockwise

What is the reference angle for -8π/3 radians?

• π/2 radians

• π/3 radians

• π/4 radians

• π/6 radians

What are the side lengths of a 60-degree reference triangle?

• (1, 2, √3)

• (2, 1, √3)

• (1, √3, 2)

• (1, 1, √2)

Which trigonometric function is the reciprocal of cosine?

• Secant

• Tangent

• Sine

• Cosecant

What is the cosine of the reference angle in the given problem?

• -√3/2

• 1/2

• √3/2

• -1/2

What is the sine of the reference angle in the problem?

• -√3/2

• √3/2

• 1/2

• -1/2

How do you rationalize the denominator of -2/√3?

• Multiply by 3/3

• Multiply by √3/√3

• Multiply by 1/√3

• Multiply by 2/2

What is the tangent of the reference angle?

• 1

• √3

• -√3

• -1

What is the cotangent of the reference angle after rationalizing?

• -1/√3

• 1/√3

• √3/3

• -√3/3